The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes of the tangent lines increase?

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

Q: Find an equation of the tangent line to the graph of f (x) = ex, where x = -1.

A: To find equation of tangent f(x)=ex at x=-1

Q: The slope of the tangent line to the graph of the function y = 7V-3 at (9, 18) is

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Q: Find an equation of the tangent line to the graph of the function                      y = arctan…

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Q: Find an equation of the tangent line to the graph of f (x) = 1/√x at x = 9.

A: The equation of the graph is given as, fx=1x We need to find the equation of the tangent to the…

Q: Find the equation for the tangent line of the graph of y = x° at (0,0).

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Q: Does any tangent line to the curve y = 2x cross the x-axis at x = -1? If so, find an equation for…

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Q: Find the equations of the tangent lines to the graph of y = ln  x  at x = 1 and x = -1.

A: To find equation of tangent lines at x=1 and x=-1f(x)=lnx

Q: What is the slope of the tangent line that touches the graph of In y + e2=-1 = 3y – 4x at the point…

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Q: Find the slope of the tangent line to the graph of y = x2 at the point where x = - 1/4.

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Q: Find an equation of the tangent line to the graph of y = f 1 (x) at x = 3, where f(x) = x 4.

A: Given: f(x)=x4 at x=3  To find the tangent line of the given function at x=3

Q: Find the slope of the tangent line to the curve of y = x 2 at the point where x = −6

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: find the equation of the tangent line to the curve when x has the given value f(x)=16/x ; x=2

A: To find the equation of tangent line to the below curve at x = 2.

Q: Find the point where the tangent line to y = x* at x 0.3 crosses the x-axis. x-intercept =

A:

Q: What is the slope of the tangent line to the graph y = a° – 3x, | at the point (x1, Y1)?

A: Our Aim is to find the slope of the tangent line to the graph y=x3-3x -(i)at the point (x1,y1),

Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

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Q: The tangent lines to the graph of f(x) =x² grow steeper as x in- creases. At what rate do the slopes…

A: Given function is, f(x)=x2

Q: Find the equation of the tangent line to the graph of f(x) = at - 5, - The equation of the tangent…

A: Given:f(x)=2x & point (-5, -25)To determine:Equation of tangent line to the graph of given…

Q: For f(x)=x3​, the instantaneous rate of change is known to be 3 at x=−1. Find the equation of the…

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Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: What is the slope of the tangent line to the graph of y=x^4-3x^2+x+2 at x=-1? [a] What is the…

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Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: Find an equation of the tangent line to the graph of fat the given point. f(x) X -

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Q: Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

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Q: Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.

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Q: Find the equation of the tangent line to the curve at the gvien value x. f(x)= (7)/(x-2); x=3

A: Given,

Q: If fx)=- has a tangent equation y/3-x+2 at x = 1, then the slope of the tangent line of f ( x) at…

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Q: The slope of the tangent line to the graph of f(x) = at a = 1 is: ¤ + x

A: Given:f(x) = xx + x

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

Q: Find the equation of the tangent line to the graph of f(x) = 1 at the point (2,1). x-1

A: Consider the graph of function, To calculate the slope (m) of the tangent line at the points (2,…

Q: Find an equation for the tangent to the curve y = at x=2

A:

Q: What is the slope of the tangent line to the graph of y-(x-1)/(x+1) at x-1?

A: We have to find

Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: ) Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

A: Given:

Q: Find the slope of the line tangent to the graph of y = tan-1 x at x = -2.

A: Given: y=tan-1x at x=-2

Q: Find the equation of the tangent line to the graph of the function f(x) =x² - Vx at the point (1,0).…

A: We know tangent is a line and the equation of a line is given by y-y0 = m(x-x0)

Q: The slope of the tangent to the curve yx + y²x² -6 at (2,1) is

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Q: Find an equation of the tangent line to the graph of y = e at the point 5,

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Q: What is the slope of the tangent line to the graph of y-(x-1)/(x+1) at x-3?

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Q: a) What is the slope of the tangent line to the graph of f at x= n ?

A: Given, fx = 4cos2x -2esin3x  We have to to find the slope of the tangent line to the graph of f at x…

Q: Find the points on the graph of f(x) = where the tangent line is horizontal. x2+2

A: Given query is to find the points where tangent is horizontal.

Q: The slope of the tangent line to the curve y=2e10xcos(-6x) at x-0 is

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Q: Find the equation of the line tangent to the graph of f(x) = (In x)* at x=7.

A: Slope is evaluated by differentiating f(x) wrt x at x=7 . Also f(7) is evaluated. Write equation of…

Q: Find all the points on the graph of y=f(x) at which the tangent line has the given slope.…

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Q: Determine the equation of the tangent line to f(x) = x3 - x, at x = 1

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Q: Find the slope of the tangent line to the graph of f(x) = √√√x-2 at x = 6. Provide your answer…

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Q: Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: